To determine which dimensions could be used for a scale model of a parking lot that is 40 meters wide and 100 meters long, we need to ensure that the scale model maintains the same aspect ratio as the actual lot.
Let's start by finding the aspect ratio of the actual parking lot:
[tex]\[
\text{Aspect Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{100 \, \text{m}}{40 \, \text{m}} = 2.5
\][/tex]
Now we'll evaluate each of the given options to see if they maintain this same aspect ratio.
Option A: [tex]\(10 \, \text{cm} \times 25 \, \text{cm}\)[/tex]
Calculate the aspect ratio for option A:
[tex]\[
\text{Aspect Ratio}_\text{A} = \frac{\text{25 cm}}{\text{10 cm}} = 2.5
\][/tex]
This option maintains the same aspect ratio as the actual parking lot.
Option B: [tex]\(100 \, \text{cm} \times 300 \, \text{m}\)[/tex]
Convert both dimensions to the same units for consistency. Note that 300 meters is significantly larger than 100 centimeters, and the units are not comparable as they stand.
[tex]\(100 \, \text{cm} = 1 \, \text{m}\)[/tex]
Hence,
[tex]\[
\text{Aspect Ratio}_\text{B} = \frac{\text{300 m}}{\text{1 m}} = 300
\][/tex]
This does not match the aspect ratio of 2.5. Therefore, this option is not valid.
Option C: [tex]\(25 \, \text{cm} \times 75 \, \text{cm}\)[/tex]
Calculate the aspect ratio for option C:
[tex]\[
\text{Aspect Ratio}_\text{C} = \frac{\text{75 cm}}{\text{25 cm}} = 3
\][/tex]
This does not match the aspect ratio of 2.5. Therefore, this option is not valid.
Option D: [tex]\(75 \, \text{inches} \times 225 \, \text{cm}\)[/tex]
First, we need to convert inches to centimeters for consistency (1 inch = 2.54 cm):
[tex]\[
75 \, \text{inches} = 75 \times 2.54 \, \text{cm} = 190.5 \, \text{cm}
\][/tex]
Now calculate the aspect ratio for option D:
[tex]\[
\text{Aspect Ratio}_\text{D} = \frac{225 \, \text{cm}}{190.5 \, \text{cm}} \approx 1.18
\][/tex]
This does not match the aspect ratio of 2.5. Therefore, this option is not valid either.
From our calculations, the only option that maintains the aspect ratio of the actual parking lot is:
Option A: [tex]\(10 \, \text{cm} \times 25 \, \text{cm}\)[/tex]
Thus, the correct dimensions for a scale model of the parking lot are given by Option A.
